Question

The temperature of a uniform rod of length L having a coefficient of linear expansion α_L is changed by ∆T. Calculate the new moment of inertia of the uniform rod about the axis passing through its center and perpendicular to an axis of the rod.

Answer 1

Moment of inertia of a uniform rod of mass and length l about its perpendicular bisector. Moment of inertia of the rod

I = `1/12"ML"^2`

Increase in length of the rod when temperature is increased by ∆T, is given by

L’ = L(1 + α_L∆T)

I’ = `"ML’"^2/12 = "M"/12"L"^2`(1 + α_L∆T)²

I’ = I(1 + α_L∆T)²